New Dialogues: Entanglement, Renormalization & Holography
Chandrasekhar Lecture ICTS, December 10, 2014 Connections: New Dialogues: Entanglement, A New Synthesis: Renormalization & Holography
Chandrasekhar Lecture ICTS, December 10, 2014 New Collisions In Physics : Entanglement, Renormalization & Holography
Chandrasekhar Lecture ICTS, December 10, 2014 New Collisions
In Physics : RemalizHi\, Holographn & Entangme
Chandrasekhar Lecture ICTS, December 10, 2014 New Collisions In Physics : Entanglement, Renormalization & Holography
Chandrasekhar Lecture ICTS, December 10, 2014 Physics of the 20th century: A grand synthesis of diverse ideas!
1927 Solvay Conference on Quantum Mechanics
in the middle of the “collision”: Do these people look happy? 1927 Solvay Conference on Quantum Mechanics
in the middle of the “collision”: Do these people look happy? Physics of the 20th century: A grand synthesis and progression of ideas! New Collisions in Theoretical Physics: Quantum Field Theory
Statistical Mechanics
Renormalization Particle Physics Group
Many Body Theory
String Theory Entanglement Holography Quantum Information
Condensed Matter Gravity Theory Renormalization: microscopic constituents Renormalization: microscopic constituents
merge to produce new collective effects merge to produce new collective effects on macroscopic scales Renormalization Group Wikipedia: “mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales”
Universality: physics at long distances is largely insensitive to details of physics at short distances Renormalization Group Wikipedia: “mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales”
Universality: physics at long distances is largely insensitive to details of physics at short distances
Why Physics Works! NOT Our World:
12 seconds! The heck with loop quantum gravity. We’ll have to try a string theory approach. Renormalization Group Flows Wikipedia: “mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales”
Effects of short-distance physics is absorbed in values of a few parameters of an effective theory
RG Flows describe how parameters of a quantum field theory change as more and more degrees of freedom at different scales are methodically “integrated out” Renormalization Group Flows Wikipedia: “mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales”
Effects of short-distance physics is absorbed in values of a few parameters of an effective theory
RG Flows describe how parameters of a quantum field theory change as more and more degrees of freedom at different scales are methodically “integrated out”
fixed points: flow is stationary “critical phenomena” Renormalization Group Flows Wikipedia: “mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales”
Effects of short-distance physics is absorbed in values of a few parameters of an effective theory
RG Flows describe how parameters of a quantum field theory change as more and more degrees of freedom at different scales are methodically “integrated out”
fixed points: flow is stationary “critical phenomena”
Conformal Field Theory (CFT): QFT with few dimensionless couplings; scale invariant theory New Collisions in Theoretical Physics: Quantum Field Theory
Statistical Mechanics
Renormalization Particle Physics Group
Many Body Theory
String Theory Entanglement Quantum Information
Condensed Matter Gravity Theory Holography Holography
• idea in quantum gravity has its origins in trying to understand paradoxes related to the realization that black holes are thermal systems emitting (almost) blackbody radiation
• Bekenstein and Hawking: black hole horizons carry entropy!! thermodynamics relativity geometry
quantum gravity Holography
• idea in quantum gravity has its origins in trying to understand paradoxes related to the realization that black holes are thermal systems emitting (almost) blackbody radiation
• Bekenstein and Hawking: black hole horizons carry entropy!! thermodynamics relativity geometry
quantum gravity • window into quantum gravity?!? Holography
• idea in quantum gravity has its origins in trying to understand paradoxes related to the realization that black holes are thermal systems emitting (almost) blackbody radiation
• Bekenstein and Hawking: black hole horizons carry entropy!! thermodynamics relativity geometry
quantum gravity • window into quantum gravity?!? • quantum gravity provides a fundamental scale Holography
• idea in quantum gravity has its origins in trying to understand paradoxes related to the realization that black holes are thermal systems emitting (almost) blackbody radiation
• Bekenstein and Hawking: black hole horizons carry entropy!!
• quantum gravity provides a fundamental scale Holography
• idea in quantum gravity has its origins in trying to understand paradoxes related to the realization that black holes are thermal systems emitting (almost) blackbody radiation
• Bekenstein and Hawking: black hole horizons carry entropy!!
• is really really small: (LHC: ) • get really big entropies!! big bag of hot gas:
black hole: Holography
• idea in quantum gravity has its origins in trying to understand paradoxes related to the realization that black holes are thermal systems emitting (almost) blackbody radiation
• Bekenstein and Hawking: black hole horizons carry entropy!!
• reminds us that entropy is associated with “heat” black hole thermodynamics • statistical mechanics also says: black hole microstates Holography
• idea in quantum gravity has its origins in trying to understand paradoxes related to the realization that black holes are thermal systems emitting (almost) blackbody radiation
• Bekenstein and Hawking: black hole horizons carry entropy!!
• statistical mechanics also says: black hole microstates “holography” suggests that the horizon is a surface that encodes information about microstates but also that dynamics and evolution of black hole can be described in terms of an effective theory living on the horizon ( ‘t Hooft; Susskind) AdS/CFT Correspondence: Bulk: Boundary: • quantum gravity • quantum field theory • negative cosmological constant • no scale (at quantum level) • d+1 spacetime dimensions • d spacetime dimensions • no gravity!
anti-de Sitter conformal space field theory
(Maldacena ‘97) AdS/CFT Correspondence: Bulk: Boundary: • quantum gravity • quantum field theory • negative cosmological constant Holography • no scale (at quantum level) • d+1 spacetime dimensions • d spacetime dimensions • no gravity!
anti-de Sitter conformal space field theory
radius energy
(Maldacena ‘97) (Freedman, Gubser, Pilch & Warner) Holographic RG flows: (Girardello, Petrini, Porrati & Zaffaroni)
• imagine potential has stationary points giving negative cosmological constant
• the gravity solution is AdS space – dual to a particular CFT
● ●
● (Freedman, Gubser, Pilch & Warner) Holographic RG flows: (Girardello, Petrini, Porrati & Zaffaroni)
• imagine potential has stationary points giving negative cosmological constant
• the gravity solution is AdS space – dual to a particular CFT
• Holographic RG flows are solutions starting at one stationary point at large radius and ending at another at small radius – connects two CFTs between high and low energies
● ● UV
IR ● Holographic RG flows:
fixed points (CFT’s) = AdS spacetimes
RG flows = geometries interpolating between asymptotic AdS regions New Collisions in Theoretical Physics: Quantum Field Theory
Statistical Mechanics
Renormalization Particle Physics Group Holographic RG Flows
Many Body Theory
String Theory Holography Quantum Information
Condensed Matter Gravity Theory Quantum Entanglement • different subsystems are correlated through global state of full system Einstein-Podolsky-Rosen Paradox: • properties of pair of photons connected, no matter how far apart they travel
“spukhafte Fernwirkung” = spooky action at a distance
Quantum Information: entanglement becomes a resource for (ultra)fast computations and (ultra)secure communications Condensed Matter: key to “exotic” phases and phenomena, e.g., quantum Hall fluids, unconventional superconductors, quantum spin fluids, . . . . Quantum Entanglement • different subsystems are correlated through global state of fully system Einstein-Podolsky-Rosen Paradox: • properties of pair of photons connected, no matter how far apart they travel
“spukhafte Fernwirkung” = spooky action at a distance
compare:
No Entanglement!!
Entangled!! Entanglement Entropy: • general diagnostic: divide quantum system into two parts and use entropy as measure of correlations between subsystems • procedure: • divide system into two subsystems, eg, A and B • trace over degrees of freedom in subsystem B • remaining dof in A are described by a density matrix • calculate von Neumann entropy:
compare:
No Entanglement!!
Entangled!! Entanglement Entropy: • general diagnostic: divide quantum system into two parts and use entropy as measure of correlations between subsystems • procedure: • divide system into two subsystems, eg, A and B • trace over degrees of freedom in subsystem B • remaining dof in A are described by a density matrix • calculate von Neumann entropy:
compare: New Collisions in Theoretical Physics: Quantum Field Theory
Statistical Mechanics
Renormalization Particle Physics Group Holographic RG Flows
Many Body Theory
String Theory Entanglement Holography Quantum Information
Condensed Matter Gravity Theory Holographic Entanglement Entropy Entanglement Entropy 2:
• in the context of holographic entanglement entropy, SEE is applied in the context of quantum field theory • in QFT, typically introduce a (smooth) boundary or entangling surface which divides the space into two separate regions • integrate out degrees of freedom in “outside” region • remaining dof are described by a density matrix calculate von Neumann entropy:
B A Entanglement Entropy 2: • remaining dof are described by a density matrix calculate von Neumann entropy:
B A R
• result is UV divergent! dominated by short-distance correlations • must regulate calculation: = short-distance cut-off
= spacetime dimension
• careful analysis reveals geometric structure, eg, (Sorkin `85; Bombelli, Koul, Lee & Sorkin `86) (Ryu & Takayanagi) Holographic Entanglement Entropy:
B A conformal field theory (Ryu & Takayanagi) Holographic Entanglement Entropy:
AdS boundary B A
gravitational AdS bulk potential/redshift spacetime
looks like BH entropy! (Ryu & Takayanagi) Holographic Entanglement Entropy: (New Horizons Prize ‘14)
AdS boundary B A
gravitational AdS bulk potential/redshift spacetime
looks like BH entropy! New Collisions in Theoretical Physics: Quantum Field Theory Statistical Mechanics
Renormalization Particle Physics ???? Group Holographic RG Flows
Many Body Theory
String Theory Entanglement Holography Quantum Information
Condensed Matter Gravity Theory Holographic Entanglement Entropy New Collisions in Theoretical Physics: Quantum Field Theory Statistical Mechanics
John Preskill (quant-ph/9904022) “Quantum information and physics: Renormalization Particle Physics some future directions” Group Holographic RG Flows
Many Body Theory
String Theory Entanglement Holography Quantum Information
Condensed Matter Gravity Theory Holographic Entanglement Entropy Zamolodchikov c-theorem (1986): • renormalization-group flows can seen as one-parameter motion:
( t = scale; )
in the space of (renormalized) coupling constants with beta-functions as “velocities”
• for unitary, Lorentz-invariant, renormalizable QFT’s in two dimensions, there exists a positive-definite real function of the coupling constants :
1. monotonically decreasing along RG flows:
2. “stationary” at fixed points : :
3. at fixed points, it equals central charge of corresponding CFT with Zamolodchikov's framework:
BECOMES with Zamolodchikov's framework:
● ●
●
●
Consequence for any RG flow in d=2: (Casini & Huerta ‘04) RG flows Meet Entanglement:
• c-theorem for d=2 RG flows can be established using unitarity, Lorentz invariance and strong subaddivity inequality:
• define:
• for d=2 CFT: (Holzhey, Larsen & Wilczek) (Calabrese & Cardy)
• hence it follows that: C-theorems in higher dimensions??
d=2:
d=4:
where and
• in 4 dimensions, have three central charges: • do any of these obey a similar “c-theorem” under RG flows? ie, C-theorems in higher dimensions??
d=2:
d=4:
where and
• in 4 dimensions, have three central charges: • do any of these obey a similar “c-theorem” under RG flows? ie, C-theorems in higher dimensions??
d=2:
d=4:
where and
• in 4 dimensions, have three central charges: • do any of these obey a similar “c-theorem” under RG flows? ie, -theorem: proposed by Cardy (1988) • numerous nontrivial examples, eg, perturbative fixed points (Osborn ‘89), SUSY gauge theories (Anselmi et al ‘98; Intriligator & Wecht ‘03) • holographic field theories with Einstein gravity dual (Freedman et al ‘99; Giradello et al ‘98) • progress stalled; no proof found; . . . . • past few years have seen a resurgence of interest and rapid progress C-theorems in higher dimensions?? past three years have seen a resurgence of interest and remarkable progress: • RG flows in generalized holographic models with higher curvatures (RM & Sinha ‘10) found new holographic c-theorem:
where C-theorems in higher dimensions?? past three years have seen a resurgence of interest and remarkable progress: • RG flows in generalized holographic models with higher curvatures (RM & Sinha ‘10) found new holographic c-theorem:
where
matches A-type trace anomaly for even dimensions (ie, a for d=4)
agrees with Cardy’s conjecture!! C-theorems in higher dimensions?? past three years have seen a resurgence of interest and remarkable progress: • RG flows in generalized holographic models with higher curvatures (RM & Sinha ‘10) found new holographic c-theorem:
where
matches A-type trace anomaly for even dimensions (ie, a for d=4)
agrees with Cardy’s conjecture!! identify C-function with universal coefficient in entanglement entropy for spherical surface in any spacetime dimension d conjecture new c-theorems for odd dimensions beyond holography C-theorems in higher dimensions?? past three years have seen a resurgence and remarkable progress: • RG flows in generalized holographic models with higher curvatures (RM & Sinha ‘10) identify C-theorem for universal coefficient in entanglement entropy for spherical surface in any spacetime dimension d conjecture new c-theorems for odd dimensions beyond holography C-theorems in higher dimensions?? past three years have seen a resurgence and remarkable progress: • RG flows in generalized holographic models with higher curvatures (RM & Sinha ‘10) identify C-theorem for universal coefficient in entanglement entropy for spherical surface in any spacetime dimension d conjecture new c-theorems for odd dimensions beyond holography
• F-theorem: d=3 (or any odd d) c-theorem; “free energy” C-function; with evidence from SUSY and nonSUSY QFT’s (Jafferis, Klebanov, Pufu & Safdi ‘11) C-theorems in higher dimensions?? past three years have seen a resurgence and remarkable progress: • RG flows in generalized holographic models with higher curvatures (RM & Sinha ‘10) identify C-theorem for universal coefficient in entanglement entropy for spherical surface in any spacetime dimension d conjecture new c-theorems for odd dimensions beyond holography
• entanglement entropy and free energy approaches same (Casini, Huerta & RM ‘11)
• F-theorem: d=3 (or any odd d) c-theorem; “free energy” C-function; with evidence from SUSY and nonSUSY QFT’s (Jafferis, Klebanov, Pufu & Safdi ‘11) C-theorems in higher dimensions?? past three years have seen a resurgence and remarkable progress: • RG flows in generalized holographic models with higher curvatures (RM & Sinha ‘10) identify C-theorem for universal coefficient in entanglement entropy for spherical surface in any spacetime dimension d conjecture new c-theorems for odd dimensions beyond holography
• entanglement entropy and free energy approaches same (Casini, Huerta & RM ‘11)
• F-theorem: d=3 (or any odd d) c-theorem; “free energy” C-function; with evidence from SUSY and nonSUSY QFT’s (Jafferis, Klebanov, Pufu & Safdi ‘11)
• d=3 F-theorem proved! unitarity, Lorentz invariance & subaddivity (Casini & Huerta ‘12) C-theorems in higher dimensions?? past three years have seen a resurgence and remarkable progress: • RG flows in generalized holographic models with higher curvatures (RM & Sinha ‘10) identify C-theorem for universal coefficient in entanglement entropy for spherical surface in any spacetime dimension d conjecture new c-theorems for odd dimensions beyond holography
• entanglement entropy and free energy approaches same (Casini, Huerta & RM ‘11)
• F-theorem: d=3 (or any odd d) c-theorem; “free energy” C-function; with evidence from SUSY and nonSUSY QFT’s (Jafferis, Klebanov, Pufu & Safdi ‘11)
• d=3 F-theorem proved! unitarity, Lorentz invariance & subaddivity (Casini & Huerta ‘12) (New Horizons Prize ‘14)
• d=4 a-theorem proved! dilaton effective actions (Komargodski & Schwimmer ‘11) New Collisions in Theoretical Physics: Quantum Field Theory Statistical Mechanics
Renormalization Particle Physics c, a, F-theorems Group Holographic RG Flows
Many Body Theory
String Theory Entanglement Holography Quantum Information
Condensed Matter Gravity Theory Holographic Entanglement Entropy Physics of the 20th century: A grand synthesis and progression of ideas! New Collisions in Theoretical Physics: Quantum Field Theory Statistical Mechanics
Renormalization Particle Physics Group
Many Body Theory
String Theory Entanglement Holography Quantum Information
Condensed Matter Gravity Theory New Collisions in Theoretical Physics: Quantum Field Theory Statistical Mechanics
Renormalization Particle Physics Group
Many Body Theory
String Theory Entanglement Holography Quantum Information Condensed Matter Gravity Theory New Collisions in Theoretical Physics: Quantum Field Theory Statistical Mechanics
Renormalization Particle Physics Group QI gives new perspective on QFT and GR
Many Body Theory
String Theory Entanglement Holography Quantum Information Condensed Matter Gravity Theory New Collisions in Theoretical Physics: Quantum Field Theory Statistical Mechanics
Renormalization Particle Physics Group QI gives new perspective on QFT and GR
Many Body Theory
The BIG New Collision: String Theory QIEntanglement could be the key to unifyingHolography QFT and GR Quantum Information Condensed Matter Gravity Theory Spacetime and Entanglement • interesting clues connecting spacetime and entanglement: Bekenstein-Hawking formula encodes black hole entropy in spacetime geometry
B A Spacetime and Entanglement • interesting clues connecting spacetime and entanglement: Bekenstein-Hawking formula encodes black hole entropy in spacetime geometry appearance of “area law” in entanglement entropy (Sorkin) application of BH formula to holographic entanglement entropy
B A Spacetime = Entanglement black hole entropy is entanglement entropy (Sorkin, ….) connectivity of spacetime requires entanglement (van Raamsdonk) spacetime entanglement conjecture (Bianchi & RM) AdS spacetime as a tensor network (MERA) (Swingle, Vidal, ….) “ER = EPR” conjecture (Maldacena & Susskind) hole-ographic spacetime (Balasubramanian, Chowdhury, Czech, de Boer & Heller; RM, Rao & Sugishita; Czech Dong & Sully; ….)
B A Gravitation from Entanglement in AdS/CFT: • relative entropy: • let: reference state; perturbed state “1st law” of entanglement entropy: (Blanco, Casini, Hung & RM) Gravitation from Entanglement in AdS/CFT: • relative entropy: • let: reference state; perturbed state “1st law” of entanglement entropy: (Blanco, Casini, Hung & RM) • holographic realization: Gravitation from Entanglement in AdS/CFT: • relative entropy: • let: reference state; perturbed state “1st law” of entanglement entropy: (Blanco, Casini, Hung & RM) • holographic realization:
• apply 1st law for spheres of all sizes, positions and in all frames:
st bulk geometry satisfies 1 law of SEE linearized Einstein eq’s
(Lashkari, McDermott & Van Raamsdonk; Swingle & Van Raamsdonk; Faulkner, Guica, Hartman, RM & Van Raamsdonk) Gravitation from Entanglement in AdS/CFT: • relative entropy: • let: reference state; perturbed state “1st law” of entanglement entropy: (Blanco, Casini, Hung & RM) • holographic realization:
spacetime provides both the stage for physical phenomena and the agent which manifests gravitational dynamics
• apply 1st law for spheres of all sizes, positions and in all frames:
st bulk geometry satisfies 1 law of SEE linearized Einstein eq’s
(Lashkari, McDermott & Van Raamsdonk; Swingle & Van Raamsdonk; Faulkner, Guica, Hartman, RM & Van Raamsdonk) Gravitation from Entanglement in AdS/CFT: • relative entropy: • let: reference state; perturbed state “1st law” of entanglement entropy: (Blanco, Casini, Hung & RM) • holographic realization:
spacetime provides both the stage for physical phenomena and the agent which manifests gravitational dynamics
• apply 1st law for spheres of all sizes, positions and in all frames:
st bulk geometry satisfies 1 law of SEE linearized Einstein eq’s
(Lashkari, McDermott & Van Raamsdonk; Swingle & Van Raamsdonk; Faulkner, Guica, Hartman, RM & Van Raamsdonk) The BIG New Collision: Quantum Field Theory Statistical Mechanics QI gives new perspective on QFT and GR Renormalization Particle Physics QI could be the keyGroup to unifying QFT and GR
new theory of Quantum Info-Gravity? Many Body Theory
String Theory Entanglement Holography Quantum Information Condensed Matter Gravity Theory The BIG New Collision: Quantum Field Theory Statistical Mechanics QI gives new perspective on QFT and GR Renormalization Particle Physics QI could be the keyGroup to unifying QFT and GR
new theory of Quantum Info-Gravity? Many Body Theory
String Theory QFTEntanglement and GR challenges QI withHolography new questions Quantum new theory of Quantum Geom-Information? Information Condensed Matter Gravity Theory The BIG New Collision: Quantum Field Theory Statistical Mechanics QI gives new perspective on QFT and GR Renormalization Particle Physics QI could be the keyGroup to unifying QFT and GR
new theory of Quantum Info-Gravity? Many Body Theory
String Theory QFTEntanglement and GR challenges QI withHolography new questions Quantum new theory of Quantum Geom-Information? Information Condensed Matter Gravity Theory